Operational Investment and Capital Structure Under Asset-Based Lending

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Yasin Alan, Vishal Gaur

To cite this article: Yasin Alan, Vishal Gaur (2018) Operational Investment and Capital Structure Under Asset-Based Lending. Manufacturing & Service Operations Management 20(4):637-654. https://doi.org/10.1287/msom.2017.0670

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INFORMS is the largest professional society in the world for professionals in the fields of operations research, management science, and analytics. For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org MANUFACTURING & SERVICE OPERATIONS MANAGEMENT Vol. 20, No. 4, Fall 2018, pp. 637–654 http://pubsonline.informs.org/journal/msom/ ISSN 1523-4614 (print), ISSN 1526-5498 (online)

Operational Investment and Capital Structure Under Asset-Based Lending

Yasin Alan,a Vishal Gaurb a Owen Graduate School of Management, Vanderbilt University, Nashville, Tennessee 37203; b Johnson Graduate School of Management, Cornell University, Ithaca, New York 14853 Contact: [email protected], http://orcid.org/0000-0002-5220-7578 (YA); [email protected] (VG)

Received: March 7, 2017 Abstract. Problem definition: Banks commonly use asset-based lending (ABL) to provide Revised: June 13, 2017 loans collateralized by a borrower firm’s inventory. We study the implications of ABL Accepted: August 11, 2017 by examining how banks should determine asset-based loan terms based on firms’ oper- Published Online in Articles in Advance: ational characteristics (e.g., inventory salvage value and demand uncertainty) and how May 24, 2018 firms should make inventory stocking and capital structure decisions under asset-based https://doi.org/10.1287/msom.2017.0670 borrowing constraints. Academic/practical relevance: Despite its widespread use for lending to small firms and those with large inventory investments, such as retailers, ABL has not Copyright: © 2018 INFORMS been well studied in the literature. Methodology: We analyze ABL using a stylized single- period screening game of incomplete information between a business owner and a bank. The bank offers a menu of loans, where each loan offer is characterized by an interest rate and inventory advance rate. The owner then decides the inventory level and the mix of debt and equity with which to finance the firm’s operations. Our model captures the practical features of ABL, for example, the bank does not have the full knowledge of the firm’s demand prospects, and the inventory advance rate leads to a credit limit that increases in the firm’s inventory investment. Results: We show that ABL enables the bank to mitigate information asymmetry by screening firms and thereby controlling each firm type’s order quantity and leverage. We also obtain hypotheses describing the equilibrium loan

contracts, capital structure, inventory investment, and bankruptcy outcomes. For instance, leverage leads to overinvestment resulting from the equity decision being endogenous to the model. Moreover, inventory advance rates are more sensitive to ﬁrms’ operational characteristics than interest rates. Managerial implications: Our study sheds light on the operational and ﬁnancial implications of ABL by demonstrating how managers should make inventory and capital structure decisions while interacting with asset-based lenders.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2017.0670.

Keywords: operations–ﬁnance interface • inventory management • capital structure • bankruptcy risk • capital market frictions

1. Introduction of capital structure in corporate finance typically do not We study the problem of a bank providing an asset- include the details of operational decisions whereas based loan to a firm that faces the newsvendor prob- the operations–finance interface models in operations lem. The firm makes an operational investment deci- management typically do not include the interaction of sion, that is, the amount of inventory to buy to meet a firm with a lender under asymmetric information or random demand, and a capital structure decision, that endogenous equity decisions. We address these ques- is, the mix of debt and equity with which to finance tions in this paper in the context of asset-based lending its operations. The bank sets the terms of the loan (ABL), which is a method commonly used by banks to offer under asymmetric information about the demand lend money to businesses. faced by the firm. This relationship necessitates a num- In ABL, a borrower firm offers its current assets, ber of questions: How does the operational investment which include its inventory, cash, and account receiv- of the firm vary with its capital structure? What loan ables, as collateral for a secured loan. The bank values terms should the bank offer to the firm? How is the the current assets and thereby sets loan terms for the equilibrium outcome affected by information asymme- firm, which consist of an interest rate and an advance try and the operational parameters of the firm, such rate for each type of current asset. The advance rate as its demand uncertainty and price–cost economics? specifies the bank’s valuation of the asset as a per- The importance of these questions is well recognized in centage of its balance sheet value. For instance, a 60% the literature, but solutions are not readily available in advance rate on inventory means that the bank is will- part because this problem falls at the interface of oper- ing to lend the firm an amount up to 60% of the pro- ations management and corporate finance. The models curement cost of its inventory. ABL is useful to banks

637 Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending 638 Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS and borrowers alike. For the bank, it mitigates the and manages its operations. The business can be of two cost of information asymmetry by imposing a credit types that differ in the distribution of demand and are limit and alleviates a problem of incomplete contract- identical in all other respects. The type of the firm is ing by giving the bank a senior right to foreclose on the known to the owner but not to the bank. firm’s assets and liquidate them in a default state (Hart Our main results are as follows. First, we find that and Moore 1998). Consequently, asset-based loans typ- the two components of the loan terms, interest rate ically require less monitoring and simpler financial and advance rate, play different roles. Interest rates pri- covenants (OCC 2014) and may carry lower interest marily respond to changes in the owner’s opportunity rates than unsecured loans (Caouette et al. 2011). These cost of equity and are relatively insensitive to newsven- features are useful to companies with large current dor model parameters, that is, demand uncertainty assets, such as retailers. They also make ABL accessi- and inventory salvage value. In contrast, advance rates ble to small businesses, which typically do not have are highly sensitive to a firm’s operational character- access to cash flow financing availed by large compa- istics. For example, with respect to the salvage value, nies with revenues in excess of $25 million and stable the average interest rate varies in the range of 10% profits (Burroughs 2008). to 11.2% whereas the average advance rate varies in ABL is a large industry. The total amount of out- the range of 45% to 95% in an extensive numerical standing asset-based loans in the United States ranged study. Thus, ABL enables the bank to screen firms and from $314 to $590 billion during 2000 to 2009 (CFA thereby control each firm type’s order quantity and 2009), which constituted about 25% of the total amount leverage. Compared with an alternative lending model of loans and short-term papers issued to nonfinan- in which the bank optimizes the interest rate with- cial corporations.1 Asset-based loans secured solely by out imposing an asset-based credit limit, we find that inventory are common in practice, especially in the ABL is most beneficial to the bank under more adverse retailing industry (Foley et al. 2012; GE Capital 1999, lending conditions, such as a low salvage value or a p. 14), which is one of the top three asset-based bor- high demand uncertainty and that ABL leads to a 23% rowers (CFA 2009). We provide specific loan examples higher expected profit for the bank, greater availability in Section3. of lending, lower interest rates, and lower bankruptcy Despite its practical usage and dependence on inven- probabilities. tory stocking decisions, ABL has not been well stud- Second, the equilibrium order quantity under lever- ied in the operations literature. A lone exception is age is always greater than or equal to that under the Buzacott and Zhang (2004), who introduce ABL to the pure equity solution. Overinvestment results exist in operations literature by studying two models: a multi- the finance literature as a result of debt holders’ inabil- period deterministic production and inventory model ity to prevent equity holders from making risky invest- of a cash-constrained firm that uses ABL and a single- ment decisions (Myers 2001 and references therein). In period stochastic inventory model in which the firm contrast, the bank in our model has the ability to pre- endowed with a starting equity makes inventory stock- vent overinvestment by offering relatively low inven- ing and borrowing decisions under ABL. Our paper tory advance rates. We find that overinvestment occurs builds on Buzacott and Zhang (2004) by introduc- despite this ability because the firm’s equity decision ing two features to fully analyze the implications is endogenous to the model. The firm’s participation of ABL. First, we endogenize the firm’s equity deci- constraint allows it to control the amount of equity sion by allowing it to jointly optimize its inventory, investment and, in the extreme, to be constituted as debt, and equity. Second, we model the game-theoretic a pure equity firm. This forces the bank to offer bet- interaction between the bank and the borrowing firm ter loan terms. As a result, leveraged firms overinvest under information asymmetry. This setting enables us at equilibrium. Furthermore, information asymmetry to study operational investment and capital structure exacerbates the bank’s problem. The bank has to offer decisions in the context of ABL. more generous loan terms to lower quality (higher de- We set up a single-period game of incomplete infor- mand variance) firms than under full information. As mation between two players, a business owner and a result, lower quality firms use more leverage and a bank. The bank moves first and offers a menu of overstock more compared with higher quality firms, loans, where each loan offer is characterized by an leading to a positive association between leverage and interest rate and an inventory advance rate. The busi- overinvestment. ness owner then decides the amount of equity to invest Finally, we demonstrate the effects of demand uncer- in the business owner’s new business, chooses a loan tainty and inventory salvage value on overinvestment, offering (if any), and makes a stocking decision to max- order quantity, leverage, and loan terms. These effects imize the business owner’s expected profit. The busi- are difficult to predict a priori because they occur ness owner sets up the business as a limited liability through two different mechanisms: the operational de- newsvendor firm, interacts with the bank on its behalf, cision and the capital structure decision. For example, Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS 639 when the firm’s demand uncertainty increases, the situations of incomplete contractibility. The analytical bank may offer less attractive loan terms, but the owner models in corporate finance generate mixed predic- may also seek to invest less equity in the firm. Thus, tions regarding the relationship between debt financ- the leverage of the firm may increase or decrease ing and investment. Among early studies, Hite (1977) with demand uncertainty. Similar puzzles arise for analyzes a setting in which debt is proportional to other metrics of interest, such as the probability of investment and finds a positive relationship between bankruptcy or the loan terms at equilibrium. We re- leverage and investment. Hite’s finding is driven by solve these questions and show how the equilibrium the absence of default risk in his model. Dotan and values of order quantity, financial leverage, and prob- Ravid (1985) show that introducing bankruptcy risk ability of bankruptcy vary across the two firm types as and treating debt as an additional decision variable well as within a firm type as the operational character- reverse Hite’s findings. In their model, an increase istics of the firm change. These results emphasize the in debt increases the cost of capital resulting from effects of operational characteristics on capital struc- bankruptcy risk. As a result, investment decreases in ture and financial distress in the context of ABL and leverage. lead to new cross-sectional and longitudinal hypothe- More generally, two opposing forces influence the ses on the operations–finance interface that may be relationship between investment and leverage. On the examined in future research. one hand, firms with high leverage may forgo prof- It is important to note that we analyze a stylized itable investment opportunities because of equity hold- model with specific assumptions. In particular, we as- ers’ unwillingness to share the benefits of an invest- sume a single-period interaction whereas, in practice, ment with debt holders. On the other hand, limited ABL may involve a multi-period relationship between liability enables equity holders to shift the downside a firm and a bank. We also assume that the bank moves risk of an investment to debt holders and thereby in- first and determines loan terms by inferring the firm’s centivizes equity holders to invest in riskier projects. best response from its demand type. However, banks Thus, debt financing may lead to underinvestment in practice typically determine loan terms based on the resulting from the debt overhang problem (Myers liquidity and quality of existing inventory collateral. 1977) or overinvestment because of risk shifting (Jensen Thus, future researchers may change the sequence of and Meckling 1976). See Myers (2001), Childs et al. moves or model the multi-period relationship between (2005) and references therein for the finance literature the counterparts to study ABL from perspectives not on the relationship between investment and leverage. captured in our model. The operations management literature has begun to address the implications of financial considerations and market imperfections on operational decisions. 2. Literature Review This is a relatively new but growing area of research. Models of capital structure in corporate finance have Xu and Birge (2004) investigate the trade-off between focused on the implications of market frictions, such bankruptcy costs and the tax benefits of debt for a as interest rate spread, taxation, costly bankruptcy, cash-constrained newsvendor endowed with exoge- and liquidity constraints, on the existence of an opti- nous equity. Their analysis shows that integrating op- mal capital structure (e.g., Modigliani and Miller 1963, erational and financial decisions can improve firm Kraus and Litzenberger 1973, Gordon 1989) and the value. Buzacott and Zhang (2004) develop a framework occurrence of a financing hierarchy under incom- to study the optimal stocking decisions of a firm when plete information (Jensen and Meckling 1976, Myers it has access to an asset-based loan. The single-period 1984, Myers and Majluf 1984, Childs et al. 2005). The model in their paper is relevant to our work. It analyzes recent literature in corporate finance has made fur- the order quantity and borrowing amount for a profit- ther advancements quantifying the impact of opera- maximizing newsvendor under ABL and bankruptcy tional characteristics of firms on their capital structure risk; equity is assumed to be exogenous, the interest through empirical evidence (for example, see Banerjee rate is fixed, and there is no information asymmetry et al. 2008 and Rauh and Sufi 2012; extensive reviews between the bank and the firm. Dada and Hu (2008) of the literature on capital structure are conducted by examine the game-theoretic interaction between a bank Harris and Raviv 1991 and Graham and Leary 2011). and a firm using a similar framework with the dif- While capital structure is affected by operational ference that the bank chooses an optimal interest rate characteristics, the opposite link also exists as capital instead of imposing a credit limit. structure choice may affect a firm’s operational invest- Besides single-period models, there has been re- ment decisions. Stiglitz and Weiss (1981) show that search on multi-period models to derive optimal inven- bank credit may be rationed at equilibrium because of tory policies under financial considerations. Hu and asymmetric information and that higher interest rates Sobel (2005) study a firm that can use short-term bor- induce firms to undertake riskier projects. Hart and rowing at a fixed interest rate in the presence of corpo- Moore (1998) show the optimality of debt financing in rate taxes and costly reorganization bankruptcy. They Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending 640 Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS

find that the firm’s capital structure is either pure debt and full information whereas the multi-period mod- or pure equity, depending on model parameters. Sim- els do not consider a firm’s game-theoretic interactions ilarly, Chao et al. (2008) analyze a self-financing (pure with lenders. Our model contributes to the operations equity) firm that faces cash flow constraints. Finally, management literature by studying these factors and Li et al. (2013) show that the joint optimization of in- demonstrating the benefits of ABL. ventory and financing decisions leads to a financing hierarchy in which the firm uses internal funds be- 3. Model fore raising external funds. Whereas the firm is typ- We analyze a single-period screening game with two ically endowed with a fixed equity in single-period players, a business owner and a commercial bank. The models, the issuance of dividends and equity have business is modeled as a newsvendor firm, which is a been included as endogenous decisions in most multi- price taker in its product market and stocks inventory period inventory models. to serve random demand. Let c denote its per unit pro- Research on the impact of financial considerations on curement cost, s the salvage value, p the selling price, operational decisions is not limited to inventory mod- q the quantity of inventory procured, and ξ the random els. Financial constraints and the risk of bankruptcy demand. The owner maximizes the owner’s expected also affect the firm’s survival strategy (Archibald et al. profit by making three related decisions: how much 2002), relations with its supply chain partners (e.g., equity and debt to have in the firm and what stocking Babich 2010, Yang and Birge 2011, Kouvelis and Zhao quantity to purchase. The first two constitute the cap- 2012), the choice of production technologies (e.g., ital structure of the firm and the third its operational Boyabatli and Toktay 2011, Chod and Zhou 2014), the investment. optimal time to shut down a firm (Xu and Birge 2006), The owner establishes the newsvendor firm with and the optimal time to offer an IPO (Babich and Sobel limited liability, which means that the owner and the 2004). Our paper is also methodologically related to firm are separate legal personalities as per corporate recent research in supply chain management that has law, and the owner’s loss is limited to the amount of dealt with mechanism design models aiming to mit- equity if the firm defaults on the loan. However, since igate the cost of information asymmetry for the less the owner makes the stocking and borrowing decisions informed party. See, for instance, Ha (2001), Yang et al. for the firm, their objectives are aligned. We use the

(2009), and Babich et al. (2012). terms newsvendor and firm interchangeably. The operations–finance interface literature also gen- The firm can be of two types denoted i 1, 2 that erates predictions regarding the impact of debt financ- differ in the distribution of demand and are identical ing on operational investment. When a newsvendor in all other respects. Let λ 0, 1 and 1 λ denote the firm’s starting equity is fixed, borrowing from a profit- probability that the firm is∈ [ of types] 1− and 2, respec- maximizing bank leads to an order quantity that is tively. We focus on a relatively common asymmetric less than the classical newsvendor solution (Buzacott information framework in which firm type is known and Zhang 2004, Dada and Hu 2008). An alterna- to the owner but not to the bank. All other model pa- tive form of debt financing, trade credit, can be more rameters are common knowledge because they can be attractive than bank loans because trade credit can im- credibly communicated to the bank whereas the de- prove supply chain coordination by creating a risk- mand forecast cannot be. For instance, the bank can sharing mechanism between a supplier and a buyer. learn the firm’s cost parameters and order quantity As a result, increasing leverage via trade credit can by auditing the firm’s financial statements and opera- lead to higher stocking quantities (Yang and Birge 2011, tions. The demand for each firm type is nonnegative Kouvelis and Zhao 2012). More recently, Chod (2017) and follows a continuous probability distribution with shows that bank financing distorts a firm’s inventory increasing failure rate (IFR). The pdf, cdf, complemen- mix because of risk shifting, and trade credit mitigates tary cdf (ccdf), and inverse ccdf of the demand distri- ¯ ¯ 1 this distortion. bution for firm type i are denoted as fi, Fi, Fi, and Fi− , Despite enhancing our understanding of capital respectively, where fi is positive on an interval and structure, the corporate finance literature typically zero elsewhere. does not include the details of operational character- Figure1 shows the sequence of events. The bank istics, decisions, and their implications for financing. moves first and offers a menu of loans αi , γi i1, 2 to As a result, it is difficult to gain operational insights the firm. Each loan offer in the menu is{( specified)} by an from the corporate finance literature. In contrast, the interest rate α and a credit limit γcq, where γ 0, 1 is operations–finance interface literature provides in- called the inventory advance rate, and cq is the∈ [ firm’s] sights into the impact of financial constraints on oper- cost of procuring inventory q. Then the owner selects ational decisions, but limited work has been done on a loan offer (or chooses not to borrow) and determines the practice of ABL. Moreover, the single-period mod- the equity, the debt, and the order quantity of the firm. els in this literature typically assume exogenous equity Then random demand is realized. If the firm’s realized Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS 641

Figure 1. (Color online) Sequence of Events for the Screening Game Played Between a Newsvendor Business Owner and an Asset-Based Lender • The firm survives High • It repays loan plus interest to the bank demand • Its remaining cash accrues to the owner

• The firm defaults The bank sets The owner Random demand Low • loan terms chooses order is realized demand The bank claims the ownership of the quantity, debt, firm’s unsold inventory and liquidates it and equity • The owner does not receive any payments from the firm due to bankruptcy demand is sufficiently high for it to avoid bankruptcy, use its inventory and equity decisions as signals of its then it salvages the excess inventory (if any), repays the true type to the bank, and the bank would set the inter- loan plus interest to the bank, and the remaining (end- est rate and advance rate based on those signals. Such ing) cash accrues to the owner. Otherwise, the bank a lending model can be studied in future research to initiates bankruptcy proceedings against the firm and examine pooling and separating equilibria under ABL. gains possession of its cash and unsold inventory. The Finally, we assume that each loan offer consists of two bank liquidates the firm’s unsold inventory to com- terms, α and γ, and is collateralized by inventory. In prac- pensate for its losses. The owner does not receive any tice, banks may include more loan conditions, such payments from the firm because of bankruptcy. as an absolute cap on the total amount of loan given. Some assumptions in our model require justification. Nevertheless, interest rate and inventory advance rate First, we set up a single-period model whereas ABL in (or an inventory-based credit limit) are the most inter- practice may involve multi-period interactions between esting and prevalent features of inventory-based loan the counterparts. A single-period model enables us to contracts in practice. For example, in 2011, Dick’s study the game-theoretic interactions between opera- Sporting Goods had a $440 million credit line at the tional and capital structure decisions while avoiding prime interest rate secured solely by inventory with an additional considerations required in a multi-period advance rate of “the lesser of 70% of eligible inven- model, such as dividends, a revolving line of credit, tory [at cost] or 85% of liquidation value of inven- and bankruptcy reorganization. Second, similar to tory.” Dillard’s had a $1 billion credit line, J.C. Penney $1.25 billion, Neiman Marcus $700 million, and Saks Buzacott and Zhang (2004), we assume that the bank is $500 million (Foley et al. 2012). See Buzacott and Zhang a monopoly. The financial economics literature shows (2004), Foley et al. (2012), and OCC (2014) for more that the bank’s market power, ranging from monopoly contract examples. Because increasing the number of (typically faced by young and small firms) to per- model parameters would complicate our model with- fect competition (typically faced by large firms), may out changing the essence of borrower–lender interac- affect firms’ access to debt financing (see Petersen and tions, we focus on a set of contracts specified as α, γ Rajan 1995 for a seminal study and Guzman 2000 for pairs. ( ) an overview of this literature). Treating the bank as a Collateralizing the loan gives the bank the legal right monopoly implies that our model is more applicable to possess and salvage the firm’s inventory in a default to small firms that typically do not have access to com- event. A good illustration of the usefulness of salvaging petitive lending. The operations–finance interface liter- inventory in ABL is provided by the bankruptcy fil- ature has both monopoly (e.g., Dada and Hu 2008) and ing and the subsequent inventory liquidation of the competitive (e.g., Xu and Birge 2004) lending models. Borders Group, Inc. Borders obtained an asset-based Accordingly, we show the robustness of our findings loan of $700 million in April 2010 from a consortium with respect to lending market competition by study- of lenders (Business Wire 2010). After its Chapter 11 ing an alternative lending model in Section B in the bankruptcy protection in February 2011 and Chap- online appendix. ter 7 liquidation in July 2011, Gordon Brothers Group Third, we assume that the bank moves first. Borrower– and Hilco Merchant Resources sold Borders’ invento- lender interactions under information asymmetry can ries at 40% to 60% discounts (Krug 2011). Our model be modeled with either the bank or the firm moving mimics this possibility because offering an asset-based first. We model a screening game to examine how the loan allows the bank to claim the ownership of the bank can use ABL to mitigate information asymmetry firm’s unsold inventory and liquidate it in case the firm by designing a menu of loan offers based on demand defaults. Foley et al. (2012) describe many such exam- types. If, instead, the firm were to move first, then we ples of ABL. The lender bank in ABL has the senior- would have a signaling game wherein the firm would most claim over the secured assets of the firm, and the Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending 642 Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS claims of other lenders (e.g., unsecured lenders or sup- firm makes capacity choice (dedicated versus flexible) pliers) are junior to it. and capital structure decisions. Alternatively, model- Since the game is sequential, we solve it by backward ing the owner’s cost of equity via CAPM makes α¯ m induction. In Section 3.1, we suppress the firm sub- a function of the covariance between the firm’s cash script i for ease of notation and characterize the firm flows and the market portfolio return, which in turn owner’s best response to a generic loan offer, α, γ . In is a function of the firm’s actions (Birge 2015). This Section 3.2, we study the bank’s problem. ( ) endogenizes the cost of equity and makes the model intractable. We leave the analysis of this more complex 3.1. The Business Owner’s Problem consideration for future research. Let x and w denote the amount of equity and debt of For the newsvendor problem to be nontrivial, we the newsvendor, respectively. To formulate the busi- assume that p > 1 + α¯ c, p > 1 + α c, and c > s. ( m) ( ) ness owner’s problem, we write the ending cash posi- 0 in (3) defines the feasible region for this problem, tion of the newsvendor as in which the first constraint specifies that the cost of procurement must be less than the starting cash avail- + + π q, x, w, ξ x w cq p min q, ξ able (i.e., debt plus equity) to the firm, the second ( ) − + { } + + s q ξ 1 + α w , (1) constraint limits the borrowing amount w to the asset- ( − ) − ( ) based credit limit γcq set by the bank, and the remain- + where max , 0 . Here, α denotes the interest rate ing constraints ensure that the firm starts its operations (·) ≡ {· } charged by the bank on the loan. If the demand ξ is with nonnegative inventory, equity, and debt. sufficiently large, the firm repays the loan plus inter- The problem (2) and (3) is a constrained nonlin- est, 1 + α w, to the bank and its ending cash position ear optimization problem. It is not concave because of ( ) accrues to the owner. Otherwise, it files for bankruptcy the imposition of limited liability. In Proposition1, we liquidation, and its cash and inventory are possessed solve this problem using the KKT conditions and show by the bank. Note that the firm’s ending cash position that it admits up to two local maxima. For this, we π q, w, x, ξ is always nonnegative because of limited first note that the firm will never borrow and hold cash ( ) liability. because of the interest levied on the loan. Moreover, The owner decides how to allocate the owner’s the firm will not hold unused equity as cash because available wealth between the newsvendor firm and of the nonnegative hurdle rate, α¯ m. Therefore, the con- other potential investments. Thus, the owner has an straint cq x + w will be binding in the firm’s optimal opportunity cost for the owner’s equity investment in solution. Substituting≤ x cq w into the problem for- the newsvendor firm because investing x in the firm mulation, we obtain an optimization− problem in two implies giving up the expected return of x from alter- dimensions, q and w, as follows: native investment opportunities available in the mar- Π∗ α, γ max EF π q, cq w, w, ξ ket. Accordingly, we treat the opportunity cost as an ( ) q, w [ ( − )] ( )∈ exogenous constant and call it as the hurdle rate. With 1 + α¯ cq w , (4) −( m)( − ) this, we solve the following owner’s problem as a func- where q, w : 0 w γcq . (5) tion of loan terms α and γ: ≡ ( ) ≤ ≤ + We simplify the objective function of this problem Π∗ α, γ max EF π q, x, w, ξ 1 α¯ m x , (2) ( ) ≡ q, x, w 0 [ ( )] − ( ) under various conditions. There can be two possible ( )∈ capital structure outcomes based on the inventory pro- where 0 q, x, w : cq x + w, w γcq, ≡ ( ) ≤ ≤ curement cost, cq, and the borrowing amount, w. In q 0, x 0, w 0 . (3) ≥ ≥ ≥ the pure equity (PE) scenario, the newsvendor does not borrow any money from the bank and finances its Here, E denotes expectation with respect to the de- F inventory investment with equity. In the debt-equity mand distribution, and α¯ 0 denotes the hurdle rate. m mix (DE) scenario, the newsvendor uses a mix of debt The owner can, in general,≥ make the owner’s deci- and equity to finance its inventory investment. We sion using a hurdle rate, a net present value (NPV) characterize the newsvendor’s expected ending cash computed with respect to the capital asset pricing position in each scenario. model (CAPM), an internal rate of return (IRR), pay- back period, or accounting rates of return. Graham and 3.1.1. Pure Equity. This scenario occurs when the constraint w 0 is binding. Setting w 0 in (4) and (5) Harvey (2001) conduct a survey of chief financial offi- ≥ cers of firms and find that hurdle rate, NPV, and IRR reveals that the owner’s problem reduces to a tradi- are the three most frequently used evaluation methods tional newsvendor problem in which the procurement cost per unit is 1+ α¯ c. Let PE q, w : w 0, q 0 . in practice with NPV being favored by large firms and ( m) ≡ {( ) ≥ } hurdle rate by small firms. Our exogenous hurdle rate The owner solves ¹ q assumption is similar to Chod and Zhou’s (2014) exoge- PE ¯ + Π max p s F ξ dξ 1 α¯ m c s q. (6) PE nous cost of equity assumption in a setting where the ≡ q ( − ) 0 ( ) − [( ) − ] ∈ Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS 643

3.1.2. Debt–Equity Mix. This scenario occurs when Let DE q, w : 0 < w γcq denote the constraint ≡ {( ) ≤ } w 0 is nonbinding so that the newsvendor finances set that ensures a debt–equity mix. Then, the owner’s ≥ its inventory investment with a mix of debt and equity. problem under DE can be written as The owner’s objective function under DE can be writ- ¹ q ten as + ΠDE α,γ max p s F¯ ξ dξ+ sq 1+α w DE DE ( )≡ q,w ( − ) d q,w ( ) [ −( ) ] π q, cq w, w, ξ ( )∈ B ( ) ( − ) + + + p min q, ξ + s q ξ 1 + α w . (7) 1 α¯ m cq w . (14) { } ( − ) − ( ) −( )( − ) In this scenario, for each q, w , there is a threshold ( ) 3.1.3. Reformulation and Solution of the Owner’s value of demand below which the firm is unable to Problem. The constraint sets of the PE and DE sce- repay the loan and interest in full. Let dB denote this narios are mutually exclusive and exhaustive subsets threshold. Setting πDE q, cq w, w, d equal to zero B of the firm’s constrained set . Further, the objective in (7) and rearranging terms( give− ) function of the DE scenario is a generalization of the + w sq + objective function of the PE scenario. These properties 1 α dB q, w [( ) − ] . (8) allow us to write the owner’s problem as follows: ( ) p s − ¹ q This threshold implies that the firm survives with + Π∗ α, γ max p s F¯ ξ dξ+ sq 1+α w probability one if it does not borrow or if the borrow- ( ) q, w ( − ) ( ) [ −( ) ] ( )∈ dB q, w ing amount is smaller than s 1+α q. Otherwise, that ( ) + + ( /( )) 1 α¯ m cq w . (15) is, when w > s 1 α q, the firm has nonzero proba- −( )( − ) bility of bankruptcy.( /( If))w s 1 + α q, then the firm’s ≤ ( /( )) ending cash position is To see how the PE scenario is subsumed in (15), note that setting w 0 in (15) leads to d q, 0 0, which s B( ) DE in turn leads to the objective function of a pure equity π q, cq w, w, ξ 0 < w + q − ≤ 1 α firm specified in (6). Thus, solving (15) is sufficient to

p s min q, ξ + sq 1 + α w. (9) find the owner’s best response to a loan offer. Hav- ( − ) { } − ( ) ing determined the objective function under different + If w > s 1 α q, then there are two scenarios. If the binding constraints, we can now show in Proposition1 ( /( )) d realized demand is less than B, then the firm declares that the owner’s objective function has at most two bankruptcy. If the realized demand exceeds d , then B local maxima. All proofs are presented in the online the firm survives and repays the loan plus interest to appendix. the bank. Thus, for w > s 1 + α q, we have ( /( )) Proposition 1. Let qPE, and qDE be the order quantities s πDE q, cq w, w, ξ w > q defined by − 1 + α + + + + p s min q, ξ sq 1 α w (10) PE 1 1 α¯ m c s (( − ) { } − ( ) ) q F¯ − ( ) − , (16) p s min q, ξ min d q, w , ξ , (11) p s ( − )( { } − { B( ) }) − 1 + γα + 1 γ α¯ c s  ¯ 1 m which equals zero when ξ dB and (9) otherwise. Tak- F− [ ( − ) ] − , ≤  p s ing expectation of (9) and (11) gives  − s  if 0 γ , DE  1 + α c E π q, cq w, w, ξ  ≤ ≤ F DE  ( ) [ ( ¹− q )] q 1 + α γc s 1 + α γc s ¯ 1 ¯ DE  p s F¯ ξ dξ + sq 1 + α w, F− ( ) − F ( ) − q   p s p s ( − ) 0 ( ) − ( )  − −  s  +  if 0 < w q,  1 α¯ m 1 γ c s ≤ 1 + α (12)  +( )( − ) , if < γ 1.   p s 1 + α c ≤  ¹ q   ¯ s − ( ) (17)  p s F ξ dξ, if w > + q. ( − ) d q, w ( ) 1 α  B ( ) The owner’s objective function defined in (15) attains up to The same expectation can be concisely written as two local maxima. First, q, w qPE, 0 is a local maxi- ( ) ( ) DE DE E πDE q, cq w, w, ξ mum if and only if α α¯ m. Second, q, w q , γcq F ≥ ( +) ( + ) [ ( −¹ q )] is a local maximum if and only if 1 α¯ m 1 α + + ( )/( ) ≥ p s F¯ ξ dξ + sq 1 + α w . (13) F¯ 1 + α γc s p s qDE , which holds trivially for ( − ) ( ) [ − ( ) ] ((([( ) − ] )/( − )) ) dB q, w α α¯ . ( ) ≤ m Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending 644 Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS

In Proposition1, qPE and qDE are the optimal order always chooses the pure equity solution because the quantities in the pure equity and debt–equity mix sce- interest rate is prohibitively high. narios, respectively. The owner’s inventory stocking Lemma 1. (i) There exists a unique interest rate threshold decision deviates from the classical newsvendor solu- α¯ that solves the equation ΠDE α,¯ 1 ΠPE, where ΠPE and tion because of adjustments to the overage and under- ΠDE α,¯ 1 are defined in (6) and( (14) ), respectively. (ii) The age costs. For instance, when a firm borrows with threshold( ) value α¯ is greater than or equal to α¯ . (iii) If the risk, that is, γ > s 1 + α c , it finances 100γ% of its m bank sets the interest rate higher than α¯, then the pure equity purchase via debt/(( and the) ) rest via equity. Then the solution, q, w qPE, 0 , is optimal for the firm regardless underage cost equals p γ 1 + α + 1 γ 1 + α¯ c, m of the inventory( ) advance( rate,) γ. which captures the effect− [ of( the) firm’s( − capital)( struc-)] ture choice on its procurement cost. The overage cost To interpret Lemma1, we first note that, for a given depends on survival. If the firm survives, buying an interest rate, the owner’s optimal expected profit is extra unit that is eventually salvaged costs γ 1 + α + nondecreasing in γ because increasing γ expands the [ ( ) 1 γ 1 + α¯ c s. If it defaults, then buying an extra feasible region of the owner’s problem. Thus, for a ( − )( m)] − unit that is eventually liquidated by the bank costs given α, the owner desires to have γ 1. On the con- 1 γ 1 + α¯ c because the firm is not obligated to trary, the owner’s optimal expected profit decreases ( − )( m) repay γ 1 + α c to the bank because of bankruptcy, but in α for a given γ, so the owner desires a low inter- ( ) it also forgoes the opportunity to salvage that unit. est rate. In Lemma1, α¯ represents the interest rate at Thus, the firm’s optimal order quantity solves which the firm owner is indifferent between creating a pure equity firm and a pure debt firm when γ 1. p γ 1 + α + 1 γ 1 + α¯ c F¯ q − [ ( ) ( − )( m)] ( ) Consequently, any interest rate that is above α¯ is pro- 1 γ 1 + α¯ cF d q, γcq hibitively high, which forces the owner to create a pure − ( − )( m) ( B( )) γ 1 + α + 1 γ 1 + α¯ c s equity firm. − [ ( ) ( − )( m)] − ¯ ¯ So far, we have shown that the firm owner chooses to F dB q, γcq F q 0. (18) ·[ ( ( )) − ( )] borrow when the interest rate is low (i.e., when α α¯ m) ≤ Rearranging terms leads to qDE formulated in (17). In and avoids borrowing when the interest rate is high (i.e., when α > α¯). What happens when α α¯ m , α¯ ? fact, (18) can be intuitively written as The owner’s capital structure choice depends∈ [ on the] 1 + γα + 1 γ α¯ c s 1 + α γc s advance rate γ. In particular, for any α α¯ , α¯ , there F¯ q [ ( − ) m] − ( ) − ∈ [ m ] ( ) p s − p s exists a threshold γ¯ α value above (below) which the − − ( ) Pr(Bankruptcy), (19) firm uses (avoids) leverage. This result is formalized in × the following lemma. where the probability of bankruptcy Pr(Bankruptcy) is Lemma 2. (i) For α α¯ m , α¯ , there exists a unique ad- a function of q. The same intuition also applies to (16) ∈ [ ] ΠDE ΠPE vance rate γ¯ α that solves the equation α, γ , as setting γ 0 (i.e., no borrowing) in (19) leads to the where ΠPE and( ) ΠDE are defined in (6) and( (14),) respec- pure equity order quantity. tively. (ii) γ¯ α increases in α α¯ , α¯ with γ¯ α¯ One of the local maxima identified in Proposition1 m m s 1 + α¯ c (and) γ¯ α¯ 1. (iii) For∈ [α α¯] , α¯ , the( owner) must be the optimal solution for the owner. We find m m borrows/(( when) ) γ γ¯(α) and creates a pure∈ [ equity] firm when that the pure equity solution, qPE, 0 , cannot be opti- ≥ ( ) ( ) γ < γ¯ α . mal when α < α¯ m because the firm’s profit is increasing ( ) in w when α < α¯ m. Intuitively, this result arises because In words, Lemma2 shows that for intermediate val- a low interest rate allows the firm to lower its cost of ues of α (i.e., when α α¯ , α¯ ), the advance rate of ∈ [ m ] capital, which makes it optimal for the firm to borrow. inventory should be sufficiently large to entice the firm

Thus, there is a single local maximum when α < α¯ m, to borrow. In fact, the threshold advance rate of inven- and the firm finances its inventory investment with a tory above which the firm borrows increases in the mix of debt and equity. The optimal solution is more interest rate. This is so because if the interest rate in- complicated when α α¯ m because there can be two creases without a compensating increase in the credit local maxima. Whether≥ the firm borrows or relies on limit, the firm eventually switches to the pure equity pure equity depends on the costs and benefits of bor- solution. rowing. On one hand, borrowing increases the firm’s Integrating Lemmas1 and2, Figure2 depicts the cost of capital, but on the other hand, it allows the owner’s optimal capital structure as a function of the owner to share the owner’s risk with the bank. In Lem- interest rate, α, and the inventory advance rate, γ. Note mas1 and2, we exploit the monotonicity properties of that the capital structure can be of different forms: pure the owner’s objective function to characterize the firm’s debt, which can take place only when γ 1; debt– best response to a loan offer when α α¯ m. Lemma1 equity mix; or pure equity. Moreover, borrowing may provides a threshold value of α above≥ which the firm or may not entail bankruptcy risk depending on the Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS 645

Figure 2. The Owner’s Capital Structure Choice as a 3.2. The Bank’s Problem Function of α and γ In this section, we first derive the bank’s profit func- 1 tion given the firm owner’s best response to a generic

loan offer. We suppress the firm subscript i in this derivation for clarity of exposition. Then we introduce firm subscripts to formulate the bank’s problem in the Risky debt-equity mix Pure equity screening game. Let κ q, w, ξ denote the bank’s profit as a function of = s/((1 + )c) the firm’s( decision) variables q, w and demand occur- () ( ) s/c rence ξ. For a given q, w pair, (8) defines a demand + ( ) +

Inventory advance rate, Riskless debt-equity mix threshold d 1 α w sq p s above (below) B ([( ) − ] )/( − ) 0 which the firm survives (defaults). When ξ dB, the 0 ≥ m firm repays the loan plus interest, 1+ α w, to the bank. Interest rate, α ( ) In contrast, if the realized demand is less than dB, Notes. We generate this figure using the following model param- the firm defaults on the loan. Consequently, the bank eters: p 2.5, c 1, s 0.2, α¯ m 0.12. Demand is Weibull with initiates bankruptcy proceedings to receive a cash ¯ k F q exp q η . We set the expected demand equal to 100 and amount of pξ and possess the ownership of the firm’s the( ) demand(−( standard/ ) ) deviation equal to 50 by setting η 112.91 and k 2.10. α¯ 0.17. unsold inventory q ξ. The bank liquidates this inventory, incurring a bankruptcy− cost because of forced value of γ. The bank has to offer a low interest rate liquidation. and/or a high advance rate to facilitate lending. Propo- Foley et al. (2012) describe the bankruptcy liquida- sition2 formalizes Figure2 and provides a full charac- tion process under ABL. Forced inventory liquidation terization of the owner’s best response to a loan offer. is typically conducted on-site, that is, in the firm’s stores, by a third-party company that specializes in Proposition 2. If α α¯ m, the owner’s best response is DE DE≤ store foreclosures. Forced liquidation is constrained to q∗, w∗ q , γcq . If α α¯ m , α¯ , the owner’s best response( ) is( ) ∈ ( ] a short time frame (e.g., 30 or 60 days) compared with the time it takes for a going concern to salvage its

( qPE, 0 , if γ < γ¯ α , unsold units. We assume for simplicity that the liq- q∗, w∗ ( ) ( ) (20) ( ) qDE, γcqDE , if γ¯ α γ 1, uidation of inventory happens at the salvage value s ( ) ( ) ≤ ≤ because the bank or the liquidator can access the same where α¯ and γ¯ α are defined in Lemmas1 and2, respec- marketplace as the firm. Nonetheless, foreclosure, legal ( ) PE tively. Finally, if α > α¯, q∗, w∗ q , 0 for all γ 0, 1 . ( ) ( ) ∈ [ ] fees, and transfer of inventory to a liquidator create Intuitively, Proposition2 implies that α < α¯ m is suf- extra costs for the bank. We model these bankruptcy- ficient for the owner to borrow. When α α¯ m , α , the related costs with an additional bankruptcy cost pro- owner chooses borrowing only when the∈ [credit] limit portional to the size of bankruptcy of the firm. is sufficiently high. Otherwise, creating a pure equity Our model can be generalized by allowing the forced firm is a better option. Finally, when the interest rate liquidation value of inventory to differ from the firm’s exceeds α¯, the owner chooses pure equity no matter salvage value s with some increase in notational com- how large the credit limit is. plexity. This generalization does not add significant 3.1.4. Remarks. The owner’s best response remains new insights because the qualitative effect of a differ- qualitatively similar when the borrowing constraint ent salvage value is similar to the impact of bankruptcy is specified as an affine function of inventory (e.g., cost. Thus, for simplicity, we use a single parameter w aq + b, where a, b > 0). Our analysis applies for for salvage value as well as forced liquidation value of such≤ a formulation as well with minor modifications inventory. to the threshold values (e.g., γ¯ α ). We set w γcq Mathematically, if a firm defaults, the bank’s profit because using a single parameter( γ)to define the≤ credit after forced liquidation can be written as limit is more consistent with practice. The owner’s best response also remains qualitatively similar when s κ q, w, ξ w > q, ξ < dB there is corporate taxation. Imposing taxes makes the 1 + α + firm more likely to borrow because interest expense pξ s q ξ b dB ξ w. (21) is tax deductible. As a result, the boundaries of the ( − ) − ( − ) − regimes depicted in Figure2 change such that the pure Here, b 0 is the bankruptcy cost per unit, and the size ≥ equity solution region shrinks. Since corporate taxa- of the bankruptcy is given by the difference between tion does not lead to significantly different insights but the bankruptcy threshold demand dB and the realized makes the analysis more cumbersome, we omit taxes demand ξ. We rewrite (21) more intuitively as con- for simplicity. sisting of two terms, the bank’s profit in case of no Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending 646 Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS default and the cost incurred by the bank because of Lemma3 reveals that the bank may lose the firm’s bankruptcy: business by setting the interest rate too high and/or setting the advance rate of inventory too low. Further- s more, it illustrates that the bank’s expected profit from κ q, w, ξ w > q, ξ < d 1 + α B firm type i is not a well-behaved function of the loan + w sq terms. This result arises in part because of the owner’s 1 α + αw p s ( ) − ξ b dB ξ (22) best response. For instance, it may be optimal for the − ( − ) p s − ( − ) 1 1 + − owner to borrow when the bank offers α[ ], γ[ ] or αw p s b dB ξ . (23) 2 2 ( ) − ( − )( − ) α[ ], γ[ ] , but this does not necessarily mean that the owner( will) also borrow under a third loan contract that Unconditional on the loan amount and the demand is a linear combination of the first two contracts (e.g., realization, we get 3 3 1 1 2 2 α[ ], γ[ ] 0.5 α[ ], γ[ ] + 0.5 α[ ], γ[ ] ) because , the ( ) ( ) ( ) i + set of α, γ values in which firm type i borrows, is not a κ q, w, ξ αw p s + b d ξ . (24) ( ) ( ) − ( − )[ B − ] convex set as depicted in Figure2. Lemma3 also shows the firm’s probability of bankruptcy as a function of This expression is equal to zero if the firm does not the loan terms and the newsvendor model parameters. borrow, equal to αw if the firm borrows and survives, Figure3 depicts the borrowing regions for two dif- and equal to (21) if the firm borrows and defaults. ferent firm types. For firm type 1 (low risk firm), the In the remainder of the paper, we use the subscript i curve that separates regions (I) and (II) is the bank’s to denote the expressions specific to firm type i. For PE indifference curve (i.e., the set of α, γ pairs such that example, qi represents the order quantity of a pure ( ) Γ1 α, γ 0) whereas the curve that separates regions equity firm under F . For i 1, 2, let q∗ α, γ , w∗ α, γ ( ) i ( i ( ) i ( )) (III) and (IV) is the owner’s indifference curve (i.e., the denote firm type i’s best response to a loan offer. This set of α, γ pairs such that Π α, γ ΠPE). That is, F F 1 1 response can be characterized by replacing with i in regions( (II)) and (III) represent the( set) of contracts that Proposition2. Accordingly, the bank’s expected profit make both the bank and the owner of a type 1 firm for firm type i 1, 2 can be written by taking expecta- better off compared with the pure equity scenario; the tion of (24) as bank loses money in (I), and the owner chooses not to

borrow in (IV) and (V). Similarly, for firm type 2 (high Γ α, γ αw∗ α, γ p s + b i i risk firm), the curve that separates regions (II) and (III) ( ) ( + ) − ( − )+ ¹ 1 α w∗ α, γ sq∗ α, γ p s ([( ) i ( )− i ( )] )/( − ) is the bank’s indifference curve whereas the curve that Fi ξ dξ. (25) · 0 ( ) separates regions (IV) and (V) is the owner’s indifference curve. The next lemma characterizes the bank’s expected Under full information, the bank would solve a sep- profit from firm type i for a generic loan offer α, γ and arate optimization problem for each firm type. Maxi- ( ) shows that it is not a well-behaved function of α, γ . mizing Γ α, γ would require the bank to pick the best ( ) i( ) α, γ pair from the set . For instance, for firm type 1 Lemma 3. Let α, γ : 0 α α¯ , 0 γ 1 ( ) i i ≡ {( ) ≤ ≤ m ≤ ≤ } ∪ α, γ : α¯ α α¯ , γ¯ α γ 1 . {( ) m ≤ ≤ i i( ) ≤ ≤ } (i) The bank’s expected profit from firm type i equals Figure 3. Borrowing Regions for Two Firm Types as a Function of α and γ

Γ α, γ 1 i( ) DE + (I) αγcqi α, γ p s b (II) (IV)  +( )−(+ − DE )  ¹ 1 α γc s p s qi α,γ  ([( ) − ] /( − )) ( ) Fi ξ dξ, if α, γ i ,  · 0 ( ) ( )∈  (III) (V) 0, otherwise. (26)

s/c (ii) Γi α, γ is not quasi-concave in α, γ . ( ) ( ) Inventory advance rate, (iii) Firm type i’s probability of bankruptcy (i.e., the 0 default probability of the loan) equals 0 m 1 2 Interest rate, α 1+α γc s +  DE Notes. We generate this figure using the following model parame- Fi [( ) − ] qi α, γ , if α, γ i ,  p s ( ) ( )∈ ters: p 2.5, c 1, s 0.2, α¯ 0.12. Demand for firm type 1 is Weibull ρi α, γ − m ( )  with mean 100 and standard deviation 50. Demand for firm type 2 is  0, otherwise. also Weibull with mean 100 and standard deviation 75. α¯ 1 0.17 and  (27) α¯ 2 0.27. Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS 647 depicted in Figure3, the bank would pick the best con- and3 show that the interest rate offered by the bank tract from regions (I), (II), and (III). However, incom- may exceed α¯ m and the firm may still borrow. Thus, the plete information regarding firm types complicates answer is unclear a priori. We answer this question in the bank’s problem because the firm type with poor the next proposition. demand prospects might choose the contract designed Proposition 4. The equilibrium order quantity, q∗ α∗, γ∗ for the firm type with good demand prospects. The i ( i i ) bank can address this shortcoming by designing a is greater than or equal to the order quantity of a pure equity firm, qPE F¯ 1 + α¯ c s p s , for i 1, 2. menu of contracts. Following the revelation principle i i((( m) − )/( − )) (Myerson 1979), we formulate the bank’s problem by The proof of the proposition shows that overinvest- focusing on direct revelation mechanisms that induce ment occurs because of a combination of limited lia- the owner to reveal the owner’s firm’s type by pick- bility and equity optimization. Limited liability creates ing a contract from the menu. Accordingly, the bank the well-known risk-shifting effect. Additionally, the offers a menu of contracts, α , γ , α , γ , with the {( 1 1) ( 2 2)} owner’s ability to adjust equity allows the owner to objective of maximizing its expected profit by lending reject any loan offers that lead to an order quantity that to firm type 1 through α , γ and firm type 2 through 1 1 is less than the pure equity order quantity. If the owner α , γ . Thus, the bank( solves) the following problem: ( 2 2) did not have this ability, the bank would have been + max λΓ1 α1, γ1 1 λ Γ2 α2, γ2 (28) able to dictate stricter loan terms (e.g., higher interest α1 , γ1 , α2 , γ2 ( ) ( − ) ( ) {( ) ( )} rates) to an equity-constrained firm, which could force s.t. Π∗ α , γ Π∗ α , γ , (29) 1( 1 1) ≥ 1( 2 2) such a firm to stock less than a firm with higher start- Π2∗ α2, γ2 Π2∗ α1, γ1 . (30) ing equity even under limited liability. The proof also ( ) ≥ ( ) reveals that overinvestment arises regardless of infor- Here, incentive compatibility constraints (29) and (30) mation asymmetry and asset-based lending. Neverthe- ensure that firm type 1 chooses α , γ and firm type 2 ( 1 1) less, those factors affect the magnitude of overinvest- chooses α2, γ2 . Participation constraints are embed- ( ) PE ment as we show in Section 4.2. ded in (29) and (30) because Π∗ α , γ Π and i i i i In the next section, we examine the effects of model Γ α , γ 0 if firm i chooses not to( borrow.) Further- i i i parameters on the equilibrium outcomes, including more,( this) formulation subsumes an alternative lend-

loan terms, leverage, order quantity, and bankruptcy ing model in which the bank offers the same loan terms occurrence. We do so numerically because of the non- to both firm types because α1, γ1 α2, γ2 is a feasible solution to (28)–(30). The next( proposition) ( ) formalizes convexity of our problem. It is well-documented in the structure of the optimal loan contracts. the literature (e.g., Rasmusen 2007, pp. 194–195) that participation and incentive compatibility constraints in Proposition 3. There exist α , γ , α , γ such that ( 1 1) ( 2 2) principal–agent frameworks make the principal’s con- both firms borrow, where firm 1 picks α1, γ1 and firm 2 straint set nonconvex, which in turn makes the princi- picks α , γ . Furthermore, the menu( of loans) that maxi- ( 2 2) pal’s problem (the bank’s problem in our setting) diffi- mizes the bank’s expected profit under information asymme- cult to analyze. When the principal’s objective function try, α∗, γ∗ , is such that γ∗ increases in α∗. {( i i )}i 1, 2 i i is well behaved, the optimal solution can be charac- Proposition3 shows that sorting through a menu of terized either in closed form or using the first order loans is feasible under ABL. In addition, if it is optimal conditions of the objective function. In our context, for the bank to sort firm types by offering two distinct a linear combination of two non-quasi-concave func- contracts, then a high (low) interest rate must be paired tions Γi α, γ , i 1, 2 makes such a characterization of with a high (low) credit limit. Its proof is straightfor- the optimal( ) solution difficult if not impossible. Thus, ward because otherwise both firm types would choose having derived the bank’s profit function and shown the loan contract with the lower interest rate and the the feasibility of a screening solution, we now numer- higher advance rate. This observation is well aligned ically examine the operational and financial implica- with practice because, all else being equal, a higher tions of ABL. credit line typically requires a higher interest rate. Does the firm stock a higher order quantity at equilibrium when it is leveraged? On the one hand, lever- 4. Managerial Insights age allows the owner to share excess inventory risk In this section, we examine the operational and finan- with the bank. This outcome can be seen in (19), where cial implications of ABL: Section 4.1 deals with the the presence of bankruptcy risk lowers the firm’s crit- effects of model parameters on the loan terms at equi- ical fractile. The existing literature suggests that this librium, Section 4.2 discusses the relationship between risk-shifting effect should lead to overinvestment. On the firm’s financial leverage and inventory investment, the other hand, the bank may be able to prevent over- Section 4.3 examines the impact of operational char- investment by setting a low inventory advance rate acteristics on financial distress, Section 4.4 compares and/or a high interest rate. For instance, Figures2 ABL with pure interest rate optimization and identifies Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending 648 Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS conditions under which ABL is most beneficial to because the loan terms consist of two components. the bank, and Section 4.5 discusses the robustness of For example, an increase in salvage value may lead to our findings with respect to alternative assumptions. an increase or a decrease in interest rate depending We conclude each subsection with empirically testable on how the advance rate changes. The other parame- hypotheses emerging from our findings. ters, such as demand uncertainty, also lead to similar The results of this section are based on a numeri- situations. cal study for a wide range of parameter values. The We find that the average interest rates offered to firm parameter combinations are as follows: salvage value s types 1 and 2 under partial information equal 10.53% ranges from 0 to 0.45 in increments of 0.05; the proba- and 15.27%, respectively, and the average advance rates bility of occurrence of firm type 1, λ, ranges from 0.1 equal 67.67% and 87.65%, respectively, across all 5,670 to 0.9 in increments of 0.1; and the hurdle rate, α¯ m, scenarios. Thus, the firm with the lower demand uncer- ranges from 0.02 to 0.18 in increments of 0.02. Demand tainty has a lower cost of borrowing and a lower lever- is modeled with a Weibull distribution with mean and age. Figures4(a) and (b) show the sensitivity of firm standard deviation µi , σi . Also let φi denote the coef- type 1’s interest rate and advance rate, respectively, to ficient of variation (cv)( of) demand for firm type i. We different model parameters. The interest rate for firm set µ1 µ2 100, σ1 φ1µ1, and σ2 2φ1µ2; that is, firm type 1 decreases in the salvage value (s), increases in type 2 has equal mean and twice the standard devia- the demand coefficient of variation (φ1), increases in tion of demand as firm type 1. We vary φ1 between 0.35 the probability that the firm is type 1 (λ), and increases and 0.5 in increments of 0.025; correspondingly, the cv in the hurdle rate (α¯ m). The advance rate for firm type 1 of demand for firm type 2, φ2, varies from 0.7 to 1.0. increases in s, λ, and α¯ m, and decreases in φ1. All other parameters are kept constant: p 1, c 0.5, The impacts of s and φi on loan terms are intuitive and b 0.1. In total, there are 5,670 unique scenarios because an increase in s or a decrease in φi makes generated from 10 values of s, nine values of λ, nine lending less risky for the bank. The impact of α¯ m is ¯ values of α¯ m, and seven values of φ1. We set the range also anticipated because an increase in αm raises the and increment for each parameter such that the stan- owner’s opportunity cost, which enables the bank to dardized values vary between 1.5 and 1.5 across all lend more at higher interest rates. However, the impact 5,670 scenarios. The standardized− values allow us to of the probability that the firm is type 1 (λ) is not intu- compare the relative sensitivity of loan terms with dif- itive. One might expect to see a negative relationship ferent parameters. For each scenario, we compute the between interest rates and λ because an increase in λ pure equity solution and the ABL equilibrium solution improves the quality of the borrowing pool. However, under full and partial information. rather than decreasing the interest rate in response to a higher λ, the bank offers a more generous advance rate 4.1. Sensitivity of Loan Terms to Model Parameters at a higher interest rate. A priori, the directional effects of changes in model An important takeaway from Figure4(a) is that the parameters on loan terms are difficult to predict equilibrium interest rate is most sensitive to the hurdle

Figure 4. The Average Equilibrium Interest Rate (a) and Inventory Advance Rate (b) for Firm Type 1 as a Function of the

Standardized Values of the Salvage Value (s), the Demand Coeﬃcient of Variation (φ1), the Probability that Firm is Type 1 (λ), and the Hurdle Rate (α¯ m ) (a) (b)

20 100 s 1 90 15 m 80

10 70

60 5 50 Equilibrium interest rate (%) Equilibrium advance rate (%) 040

–1.5 –1.0 –0.5 0 0.5 1.0 1.5 –1.5 –1.0 –0.5 0 0.5 1.0 1.5 # of standard devations from the mean # of standard devations from the mean Notes. We standardize a model parameter by subtracting its mean and dividing by its standard deviation computed across all 5,670 data points. Each data point represents the average value of the response variable for a particular standardized value of a model parameter. For instance, in (a), the data point at which the standardized α¯ equals zero represents the average equilibrium interest rate over 5,670 9 630 m / scenarios with α¯ m 10%, which is the average α¯ m in the data set. Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS 649

rate, α¯ m. To see this, observe that a one standard devi- for firm type 1 under information asymmetry. In Fig- ation increase in α¯ m raises the average interest rate ure5(a), we see that leverage and order quantity both by more than 5%, from 10.51% to 15.86%, whereas a increase when s increases. This result arises because an one standard deviation change in the salvage value or increase in s leads to a higher stocking quantity as well demand coefficient variation changes the average inter- as more lenient loan terms from the bank, which enable est rate by less than 1%. Put differently, a firm’s opera- the firm to increase both order quantity and leverage. tional characteristics (i.e., s and φi) play less significant On the contrary, Figure5(b) shows that changes in φ1 roles than α¯ m in determining the cost of borrowing. lead to a negative relationship between leverage and Unlike the interest rate, the advance rate is highly sen- order quantity. This result arises because the firm’s sitive to a firm’s operational characteristics. This leads stocking quantity increases in φ1 but the bank offers to a hypothesis that may be tested in future empiri- less attractive loan terms to the firm. cal research: interest rates under ABL are more sensi- The extent of overinvestment by the firm, compared tive to hurdle rate than to operational characteristics with the pure equity solution, is also influenced by the of firms whereas advance rates are more sensitive to salvage value and demand uncertainty. We find that operational characteristics of firms. a higher salvage value leads to declining overinvest- Analyzing the sensitivity of the loan terms to model ment as both order quantity and leverage increase but parameters for firm type 2 leads to similar insights and the risk-sharing benefit of limited liability becomes less is omitted for brevity. valuable to the firm. Specifically, a one standard deviation increase in s decreases the average overinvestment 4.2. Financial Leverage and Order Quantity level (i.e., percentage deviation from the pure equity We showed in Proposition4 that a firm stocks more order quantity) from 21.35% to 17.13% for firm type 2 inventory at equilibrium when it is leveraged than under information asymmetry. On the other hand, a when it chooses a pure equity solution. That proposi- higher demand uncertainty leads to increasing over- tion was driven by a combination of limited liability investment as limited liability becomes more valuable and the owner’s ability to optimize equity. We exam- to the firm; a one standard increase in φ2 increases ine two further aspects of financial leverage and order the average overinvestment from 20.11% to 22.60% for quantity in this section: the effect of model param- firm type 2 under information asymmetry. Thus, to eters and the effect of screening through a menu of summarize, the equilibrium order quantity and the asset-based loans. By varying the model parameters, extent of overinvestment may increase or decrease with we observe how the financial leverage and order quan- leverage for a firm depending on which underlying tity for a given firm type can change as a function operational parameter varies: salvage value or demand of the firm’s operational characteristics. By comparing uncertainty. across the two firm types, we observe how the financial Another way to examine the leverage–order quantity leverage and order quantity vary across a cross-section relationship is through the effect of screening under of firms. information asymmetry. Table1 reports the average Figure5 shows financial leverage and order quantity leverage ratios, order quantities, and extent of over- as functions of salvage value and demand uncertainty investment by firms across the 5,670 scenarios in our

Figure 5. Order Quantity and Leverage as a Function of Salvage Value (a) and Demand Coeﬃcient of Variation (b) for Firm Type 1 Under Information Asymmetry (a) (b)

1.0 120 0.80 Order quantity 140 Leverage 0.9 115 0.75 0.8 120 0.7 110 0.70 Leverage 100 0.6 Leverage Order quantity Order quantity 105 0.65 0.5 80 0.4100 0.60

0 0.1 0.2 0.3 0.4 0.35 0.40 0.45 0.50 Salvage value Demand coefficient of variation Notes. Each data point in (a) represents an average of 5,670 10 567 scenarios with the same s value. Similarly, each data point in (b) represents an average of 5,670 7 810 scenarios with the same φ value./ / 2 Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending 650 Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS

Table 1. The Relationship Between Leverage and Overinvestment Across the Cross-Section of Firms with Varying Demand Uncertainty

Full information Partial information

Firm Leverage (%) Order qty. Overinvestment (%) Leverage (%) Order qty. Overinvestment (%)

1 99.53 114.18 4.20 67.67 110.91 0.93 2 87.01 117.54 15.67 87.65 121.08 19.80

Notes. The leverage columns report the average debt-to-assets ratios computed across all 5,670 data points. The overinvestment columns report the average percentage deviation from the pure equity solution across all 5,670 data points. analysis. (Here, we compare the amounts of overinvest- 4.3. Operational Parameters and the ment because the two firm types have different optimal Probability of Bankruptcy order quantities in pure equity solutions so that their The average probability of bankruptcy of firm type 1 order quantities cannot be compared directly.) Under across all scenarios is 2.71% and of firm type 2 is 26.75% full information, firm type 1 has higher leverage than under partial information. Under full information, the firm type 2 (99.5% versus 87.0%) because firm type 1 corresponding values are 10.28% and 26.87%, respec- has lesser demand uncertainty and the bank offers tively. Moreover, our model enables us to examine more attractive loan terms to firm type 1, consisting of the effects of operational characteristics (i.e., demand a lower interest rate and a higher advance rate. Under uncertainty and inventory salvage value) on a firm’s information asymmetry, the bank is forced to sort the bankruptcy risk. firms on interest rate and advance rate. As a result, firm The classical inventory models imply that an in- type 1 has lower leverage (67.7% versus 87.7%) and also crease in demand uncertainty makes it more challeng- overinvests by less than firm type 2. Thus, screening ing to match supply with demand, which in turn might leads to a positive relationship between leverage and make bankruptcy risk more prevalent because of more overinvestment across the cross-section of firms. volatile cash flows. Thus, one might infer a positive relationship between demand uncertainty and finan- While the lender’s inability to control the borrower firm’s actions and risk-shifting incentives are known cial distress. However, a firm’s capital structure may in the literature to cause overinvestment, it is interest- also change with demand uncertainty. As discussed in ing to note that the bank in our model has the ability Section 4.1, the equilibrium advance rate decreases in demand uncertainty. Consequently, the firm is forced to minimize or even prevent overinvestment by offer- to use less leverage, which might lead to a negative ing relatively low advance rates. For instance, when relationship between demand uncertainty and finan- s > 0, setting α , γ α¯ , s 1 + α¯ c would force ( i i) ( m /(( m) )) cial distress. Figure6(a) examines these counterclaims both firm types to stock their pure equity order quanti- for firm type 2 and shows that the probability of ties while allowing the bank to make money. However, bankruptcy increases in the demand coefficient of vari- the pure equity order quantities are too small to max- ation under both full and partial information. A case- imize the bank’s expected profit. Screening through by-case analysis of the 5,670 scenarios reveals that the ABL enables the bank to maximize its expected profit demand threshold below which the firm is bankrupt but at the cost of encouraging overinvestment by firm decreases in demand uncertainty because of a decline type 2. in the advance rate. However, this decrease is insuffi- In summary, we find that the relationship of finan- cient to offset the increase in the probability of expe- cial leverage with order quantity and overinvestment riencing relatively low demand realizations. Thus, we is driven by limited liability, screening through a find that a higher demand uncertainty leads to a higher menu of asset-based loans, and variation in underly- bankruptcy risk under ABL. ing model parameters. We find that (i) a firm orders Similarly, salvage value, s, may also lead to coun- more inventory under leverage than under pure equity. tervailing arguments. All else being equal, an increase (ii) Order quantity and financial leverage increase and in s should lead to a lower probability of bankruptcy overinvestment decreases with an increase in salvage because such an increase enables the firm to recover value for a firm. (iii) Order quantity increases, lever- from a low demand realization by selling its unsold age decreases, and overinvestment increases with an inventory at a relatively small discount. However, increase in demand uncertainty for a firm. (iv) Under the classical newsvendor model suggests that a firm information asymmetry, screening through ABL leads should stock more when s is high. Furthermore, the to a positive correlation between leverage and overin- equilibrium inventory advance rate increases s as doc- vestment across the cross-section of firms with varying umented in Section 4.1. Consequently, an increase in s demand uncertainty. enables the firm to use more leverage and stock more, Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS 651

Figure 6. The Average Equilibrium Probability of Bankruptcy of the High-Risk Firm (Firm Type 2) as a Function of Its Demand Coeﬃcient of Variation (a) and the Salvage Value (b) (a) (b)

0.30 0.30

0.28 0.28

0.26 0.26

0.24 0.24

Bankruptcy probability 0.22 Bankruptcy probability 0.22 Full information Partial information 0.20 0.20

0.70 0.80 0.90 1.00 0 0.1 0.2 0.3 0.4 Demand coefficient of variation Salvage value which may lead to a higher bankruptcy risk. Figure6(b) separating equilibrium in which one firm type chooses shows that the relationship between salvage value pure debt and the other chooses pure equity. Finally, and bankruptcy risk is nonmonotone because of these if αPIRO > max α¯ , α¯ , then we have a pooling equilib- { 1 2} opposing forces. Thus, we find that a high salvage rium in which both firm types choose pure equity. The value does not necessarily lead to a lower bankruptcy last outcome arises when the bank’s expected profit is risk under ABL. negative for all interest rates at which the firms borrow. In summary, the probability of bankruptcy increases In such scenarios, the bank sets the interest rate above in demand uncertainty. It is nonmonotone in salvage max α¯ 1, α¯ 2 to make borrowing unattractive to both

{ } value, being first increasing and then decreasing when firm types. One sufficient condition for the existence of salvage value is large enough. this outcome is a high bankruptcy cost b, which does not affect the owner’s best response for a given α, but 4.4. When Is ABL Most Beneficial to the Bank? increases the bank’s loss in case of firm default. We compare the effectiveness of ABL with respect to Under ABL, the bank lends to both firm types in pure interest rate optimization (PIRO), which has been all 5,670 scenarios. Under PIRO, it lends to both firm commonly used as a lending model in the literature types in 2,907 scenarios, only to firm type 2 in 1,701 for settings with complete information and exogenous scenarios, and to neither firm (i.e., the lending mar- equity (e.g., Xu and Birge 2004, Dada and Hu 2008, ket collapses) in the remaining 1,062 scenarios. The Boyabatli and Toktay 2011). average ABL equilibrium interest rates offered to firm PIRO is a special case of our model obtained by set- types 1 and 2 under partial information equal 10.53% ting the advance rate γ 1. From Figure2, it follows and 15.27%, respectively. In contrast, the equilibrium that the firm’s best response will be either pure debt or interest rate offered by the bank under PIRO is 19.25% pure equity. This result arises because the owner makes on average but can be as high as 53.81%. The loan sizes both equity and debt decisions in our model. More- are smaller under ABL. By focusing on the scenarios in over, low interest rate contracts are strictly better than which borrowing takes place, the average loan sizes of high interest rate contracts for both firm types, so the firm types 1 and 2 under PIRO equal 58.61 and 70.89, bank cannot benefit by offering a menu of interest rates. respectively. Under ABL, the corresponding amounts Instead, it optimizes on a single interest rate under are 50.34 and 60.13, respectively. information asymmetry. This simplifies the problem The bank’s average expected profit is 3.28 under considerably. PIRO and 4.05 under ABL, which is an increase of 23%. Let αPIRO denote the bank’s optimal interest rate Firm type 1’s profit is equal to its reservation pay- under PIRO. From Proposition2, α¯ i is the maximum off, that is, the pure equity expected profit, in all sce- interest rate at which firm i borrows. The bank’s objec- narios for both ABL and PIRO. Firm type 2’s profit tive function has jump discontinuities at α α¯ i, i 1, 2, is 6.71% higher on average than its pure equity profit where firm type i switches from pure debt to pure under ABL and 10.85% higher under PIRO. Thus, firm equity. If αPIRO min α¯ , α¯ , then we have a pool- type 2 enjoys an information rent because of informa- ≤ { 1 2} ing equilibrium in which both firm types choose pure tion asymmetry. ABL reduces the amount of informa- PIRO debt. If α lies between α¯ 1 and α¯ 2, then we have a tion rent. Comparing the scenarios where both firm Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending 652 Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS

Figure 7. The Comparison of the Bank’s Expected Proﬁt Under ABL and PIRO as a Function of the Salvage Value (a), Firm Type 1’s Demand Coeﬃcient of Variation (b), and the Probability that Firm Is Type 1 (c) Under Information Asymmetry (a) (b) (c) 8 5.0 5.0 ABL PIRO 4.5 4.5 6 4.0 4.0

4 3.5 3.5

3.0 3.0 2 2.5 2.5

The bank’s expected profit 0 The bank’s expected profit 2.0 The bank’s expected profit 2.0 0.0 0.1 0.2 0.3 0.4 0.35 0.40 0.45 0.50 0.2 0.4 0.6 0.8 Salvage value Demand coef. of var. of firm type 1 The probability that firm is type 1

Note. We use the entire data set to compute the bank’s average equilibrium expected profit under ABL and PIRO for each value of s, φ1, and λ. types borrow, the order quantity under ABL is 0.93% equity order quantity. Interestingly, the bank lends a higher than the pure equity solution for firm type 1 and smaller average amount at a lower interest rate but 19.80% higher for firm type 2; under PIRO, the corre- makes a higher average profit under ABL than under sponding amounts are 1.82% and 30.11%, respectively. PIRO. Our numerical analyses lead to the following The average bankruptcy probabilities for firm types 1 hypotheses: (i) Asset-based loans have lower interest and 2 are 2.71% and 26.75% under ABL and 4.64% and rates compared with pure interest rate loans. (ii) Asset- 29.57% under PIRO. based loan arrangements are more likely to emerge The superiority of ABL for the bank is not surprising under more adverse lending circumstances (e.g., high because the bank’s optimal contract under PIRO is a demand uncertainty, low salvage value) as compared feasible solution to its problem under ABL. Nonethe- with pure interest loans. less, it is not clear a priori when ABL would be more beneficial to the bank. Figure7 examines the 4.5. Robustness Checks We checked the robustness of our numerical results bank’s expected profit under ABL and PIRO for var- with respect to lending market competition and infor- ious parameter values. Figure7(a) shows that ABL is mation asymmetry based on mean demand. Analyzing more beneficial when the salvage value is low. A priori, ABL in a competitive lending market setting revealed we might expect the opposite because a high salvage that competition does not change our main insights. value enables the bank to recover its losses in case of Furthermore, a comparison of outcomes under com- default. However, in this situation, both PIRO and ABL petitive and monopoly lending yields the following perform well. Figure7(b) demonstrates the impact of hypotheses: (i) Lending market competition leads to the demand coefficient of variation of firm type 1, φ1, more overinvestment by borrower firms than lending on the performance gap. We find that ABL is more from a monopoly bank. (ii) Lending market competi- beneficial when demand volatility is high. Finally, Fig- tion leads to significantly lower interest rates but has ure7(c) demonstrates that the benefits of ABL are more only a small effect on advance rates compared with pronounced when the probability of occurrence of firm monopoly lending. We report our competitive lending type 1, λ, is relatively low. Thus, ABL is more advan- market analysis in Section B in the online appendix. tageous when the bank is less likely to face firm type 1 In addition, we replicated our numerical study for an because adverse selection is more severe and lending alternative setting in which the two firm types have the is more risky. same standard deviation of demand but differ in mean In summary, ABL is superior to PIRO in many re- demand. Although these two settings do not allow spects. The undesirable consequences of PIRO, such apples-to-apples comparison, our qualitative insights as excessive borrowing, clustering of firms to two ex- remained unchanged with one exception. Namely, the treme capital structure outcomes (i.e., pure debt and third hypothesis in Section 4.2 is changed. Whereas pure equity), prohibitively high interest rates, and a that hypothesis states that the order quantity increases potential market collapse, vanish under ABL. More- with demand uncertainty, we observe that the order over, the bank lends to both firm types, which mitigates quantity increases with average demand when we keep adverse selection and increases the bank’s expected the demand standard deviation constant and vary the profit. Both firm types borrow at lower interest rates average demand across the two firm types. Thus, the and make stocking decisions that are closer to the pure order quantity increases in the demand cv in our Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS 653 original numerical study whereas it decreases in the of ABL such as multi-period interactions and loan demand cv in the new study. All other hypotheses are terms that are based on existing collateral. Thus, future supported in the new study. Our analysis, which we do research can study ABL under alternative decision not report in the paper because of space limitations, is frameworks. For instance, the interaction between the available upon request. firm and the bank can be modeled as a signaling game instead of a screening game to allow the bank to move 5. Conclusions after observing the firm’s decisions and collateral. Sim- ilarly, studying ABL in a multi-period setting maybe Our paper puts the classical newsvendor model in a useful to illustrate how the firm’s inventory position broader context in a novel setting of ABL. It provides and revolving line of credit change over time. In addi- insights regarding the different roles played by inter- tion, the owner’s interactions with financial markets est rate and advance rate in a loan offer, the benefits of can be enriched by allowing trading between the bank ABL, the relationship between leverage and overinvest- and the owner or enabling the owner to solve a CAPM- ment, and the effect of operational characteristics on based portfolio optimization problem with multiple the equilibrium through inventory and capital struc- investment opportunities. Finally, it will be fruitful to ture decisions. examine our model’s predictions regarding the opera- Comparing our results with those in the litera- tional and financial implications of ABL using data. ture, we find that they differ mainly because of the effect of endogenous equity decisions. Dada and Hu Acknowledgments (2008) show that, in an interaction between a capital- The authors thank the editors, Chris Tang and Brian Tomlin; constrained newsvendor and an interest rate–optimiz- anonymous referees; colleagues at Cornell University and ing bank, there is a threshold starting equity value Vanderbilt University; and many attendees at our talks for below which the firm is financed via a mix of debt and thoughtful comments that helped improve our manuscript. equity, and the equilibrium order quantity is less than the classical newsvendor quantity. Their model is a spe- Endnote cial case of our model with a fixed starting equity x, full 1 Commercial Finance Association, the trade association for asset- information, and s 0, b 0, α¯ m 0, and γ 1. Our based lenders, publishes annual and quarterly ABL surveys, which are available at http://www.cfa.com. See Federal Reserve (2010, p. 66, analysis implies that endogenizing the equity decision in the same context leads to an extreme capital structure line 39) and earlier reports for the total amount of loans and short- term papers issued to nonfinancial corporations. outcome (pure debt or pure equity) and that the equilibrium order quantity is greater than the pure equity References order quantity because of the firm’s ability to optimize Archibald TW, Thomas LC, Betts JM, Johnston RB (2002) Should its equity. Similarly, Buzacott and Zhang (2004, p. 1285) start-up companies be cautious? Inventory policies which max- state, imise survival probabilities. Management Sci. 48(9):1161–1174. Babich V (2010) Independence of capacity ordering and financial From our analysis above, it is not difficult to see that if subsidies to risky suppliers. Manufacturing Service Oper. Manage- the bank has the freedom of choosing the appropriate ment 12(4):583–607. interest rate for each retailer it serves, it can find an opti- Babich V, Sobel MJ (2004) Pre-IPO operational and financial deci- mal interest rate for each individual retailer based on sions. Management Sci. 50(7):935–948. the retailer’s wealth level and maybe other parameters Babich V, Li H, Ritchken P, Wang Y (2012) Contracting with asymmetric demand information in supply chains. Eur. J. Oper. Res. associated with each retailer (demand distribution, cost 217(2):333–341. structure, etc.). Hence, interest rate alone is sufficient to Banerjee S, Dasgupta S, Kim Y (2008) Buyer–supplier relation- guarantee optimal bank returns. ships and the stakeholder theory of capital structure. J. Finance 63(5):2507–2552. In contrast, we show that interest rate optimization can Birge JR (2015) OM forum—operations and finance interactions. be insufficient to maximize the bank’s expected profit Manufacturing Service Oper. Management 17(1):4–15. when equity is an endogenous decision for the owner Business Wire (2010) GE Capital is co-lender in a $700 million credit and the use of ABL is beneficial even in settings where facility to Borders. Accessed October 5, 2014, https://www .businesswire.com/news/home/20100409005521/en/GE-Capital-Co the bank has the freedom of optimizing the interest -Lender-700-Million-Credit-Facility. rate under full information. Thus, endogenizing the Boyabatli O, Toktay B (2011) Stochastic capacity investment and flexi- owner’s equity decision significantly affects model pre- ble vs. dedicated technology choice in imperfect capital markets. dictions in settings where a firm makes joint ordering Management Sci. 57(12):2163–2179. Burroughs G (2008) Asset-based loans can offer attractive financing and capital structure decisions. option. Puget Sound Bus. J. (April 27), https://www.bizjournals Our paper falls in a rich area of research. It captures .com/seattle/stories/2008/04/28/focus11.html. some practical aspects of ABL, such as the inventory Buzacott JA, Zhang RQ (2004) Inventory management with asset- advance rate, the possession and liquidation of inven- based financing. Management Sci. 50(9):1274–1292. Caouette JB, Altman EI, Narayanan P, Nimmo R (2011) Manag- tory collateral by the bank, and information asymme- ing Credit Risk: The Great Challenge for Global Financial Markets, try. However, it also leaves out other practical aspects 2nd ed. (John Wiley & Sons, Hoboken, NJ). Alan and Gaur: Operational Investment and Capital Structure Under Asset-Based Lending 654 Manufacturing & Service Operations Management, 2018, vol. 20, no. 4, pp. 637–654, © 2018 INFORMS

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